A novel upwind stabilized discontinuous finite element angular framework for deterministic dose calculations in magnetic fields.

A novel upwind stabilized discontinuous finite element angular framework for deterministic dose calculations in magnetic fields.
Phys Med Biol. 2017 Dec 19;:
Authors: Yang R, Zelyak O, Fallone BG, St-Aubin J
Abstract
Angular discretization impacts nearly every aspect of a deterministic solution to the linear Boltzmann transport equation (LBTE), especially in the presence of magnetic fields, as modeled by a streaming operator in angle. In this work a novel stabilization treatment of the magnetic field term is developed for an angular finite element discretization on the unit sphere, specifically involving piecewise partitioning of path integrals along curved element edges into uninterrupted segments of incoming and outgoing flux, with outgoing components updated iteratively. Correct order-of-accuracy for this angular framework is verified using the Method of Manufactured Solutions for linear, quadratic, and cubic basis functions in angle. Higher order basis functions were found to reduce the error especially in strong magnetic fields and low density media. We combine an angular finite element mesh respecting octant boundaries on the unit sphere to spatial Cartesian voxel elements to guarantee an unambiguous transport sweep ordering in space. Accuracy for a dosimetrically challenging scenario involving bone and air in the presence of a 1.5 T parallel magnetic field is validated against the Monte Carlo package GEANT4. Accuracy and relat...

Source: Physics in Medicine and Biology - December 19, 2017 Category: Physics Authors: Yang R, Zelyak O, Fallone BG, St-Aubin J Tags: Phys Med Biol Source Type: research